Math Course Descriptions

Mathematics Courses for Non-Majors

MA 9 and MA 10 Mathematics for Liberal Arts
This course presents major mathematical concepts in a historical and cultural setting. Topics include geometry, set theory logic, and differential and integral calculus. Students explore the interplay between mathematics, philosophy, and the arts in addition to the more traditional relationship between mathematics and the physical sciences. The course treats mathematics as an art for its aesthetic beauty and as a science, providing a mathematician's view of the subject rather than preparing students for a specific application of mathematics. Three credits.

MA 17 Introduction to Probability and Statistics
This introduction to the theory of statistics includes measures of central tendency, variance, Chebyshev's theorem, probability theory, binomial distribution, normal distribution, the central limit theorem, and estimating population means for large samples. Students who have taken two semesters of calculus may not take this course. Three credits.

MA 19 Introduction to Calculus
This course introduces differentiation and integration, and shows how these ideas are related. The course illustrates how a huge array of important and interesting geometry, application, and life questions, when expressed in the language of functions, turn out to be questions about derivatives and integrals, and are amenable to the same body of techniques and universal principles. The course presents the basic concepts numerically, algebraically, and geometrically, using graphing calculators to illustrate many of the underlying geometrical ideas. MA 19 is not a prerequisite for any other course; students who have received credit for MA 19 may not take MA 121 for credit. Three credits.

MA 27 Intermediate Statistics
This course covers the tools and techniques of statistics most commonly seen in business applications and meets the third semester of the Dolan School of Business's quantitative requirement. Topics include (multi)linear regression and correlation; inference, including t-tests and chi-square tests; and analysis of variation. Students who have taken MA 121-122 or MA 171-172 should take MA 217. (Prerequisites: MA 17, MA 19) Three credits.

MA 121 Applied Calculus I
Topics in this course include: plane analytic geometry; foundations of the calculus; differentiation of algebraic functions; extrema and curve sketching; and applications of derivatives. Formerly listed as MA 21. MA 121 is not a prerequisite for MA 171; students who received credit for MA 121 may not take MA 171 for credit. Three credits.

MA 122 Applied Calculus II
Topics in this course include antiderivatives; the Fundamental Theorem of Calculus; differentiation and integration of trigonometric, logarithmic, and exponential functions; techniques of integration; and applications of the definite integral. Formerly listed as MA 22. MA 122 is not a prerequisite for MA 171; students who have received credit for MA 122 may not take MA 172 for credit. (Prerequisite: MA 121 or equivalent) Three credits.

MA 125 Calculus I: Engineering and Physics Majors
This course covers analytic geometry, continuous functions, derivatives of algebraic and trigonometric functions, product and chain rules, implicit functions, extrema and curve sketching, indefinite and definite integrals, and applications of derivatives and antiderivatives. Formerly listed as MA 25. Three credits.

MA 126 Calculus II: Engineering and Physics Majors
This course covers exponential and logarithmic transcendental functions, their derivatives and their integrals; the Fundamental Theorem of Calculus; applications to area, arc length, and volumes of revolution; hyperbolic functions, inverse trigonometric functions; methods of integration by substitution and parts; and indeterminate forms and improper integrals. Formerly listed as MA 26. (Prerequisite: MA 125 or equivalent) Three credits.

MA 211 Applied Matrix Theory
Students majoring in the sciences, economics, and business learn techniques and applications of linear algebra and solve linear equations, determinants, linear geometry, eigenvalues, and eigenvectors. Closed to mathematics majors. Three credits.

MA 217 Accelerated Statistics
This introductory, calculus-based statistics course focuses on applications in business, statistics, and everyday events. Topics include descriptive statistics including mean, median, mode, standard deviation, histograms, distributions, box plots, and scatter plots; probability theory including counting rules, random variables, probability distributions, expected values, binomial and normal distributions, and the central limit theorem; inferential statistics including point estimates, confidence intervals, and hypothesis testing; and regression theory. Students learn to analyze data with the aid of common software packages. (Prerequisites: MA 121, MA 122) Three credits.

MA 225 Applied Calculus III
This course covers partial differentiation, multiple integrals, infinite series, and first order differential equations. (Prerequisites: MA 121, MA 122) Three credits.

MA 227 Calculus III: Engineering and Physics Majors
Topics in this course include infinite series, tests for convergence, power series, Taylor series; geometry in three-space; partial differentiation of continuous functions; chain rule, exact differentials, maxima and minima; multiple integration; application to volumes, center of gravity; and polar, cylindrical, and spherical coordinates. (Prerequisite: MA 126 or equivalent) Three credits.

MA 228 Calculus IV: Engineering and Physics Majors
Topics in this course include: vector arithmetic and algebra, dot and cross products, parametric equations, lines and planes; gradient, directional derivative, curl, divergence; line integrals, work, Green's theorem, surface integrals; Stokes's and divergence theorems. (Prerequisite: MA 227 or equivalent) Three credits.

MA 321 Ordinary Differential Equations
This course presents solutions of first and second order differential equations by formal methods; linear equations in detail; systems of equations; series solutions; and applications to geometry and physics. (Prerequisite: MA 225 or equivalent) Three credits.

MA 322 Partial Differential Equations with Special Functions
Topics in this course include solution of constant and variable coefficient linear equations; Lagrange method using subsidiary equations; separation of variables in two and three variables; eigenvalue problems; Fourier series solution of the heat equation, the wave equation, and the Laplace equation; Gamma and Bessel functions; Legendre, Hermite, and Laguerre polynomials; and calculus of variations. (Prerequisite: MA 321 or equivalent) Three credits.

Mathematics Courses for Majors

MA 171 Differential Calculus
Students learn functions; limits, continuity, and derivatives; applications; relative maxima, minima, and curve sketching; absolute maxima and minima; related rates; Rolle's Theorem and the mean value theorem. Four credits.

MA 172 Integral Calculus
This course presents anti-differentiation; the definite integral and the Fundamental Theorem of Calculus; applications; area, volume, and arc length; exponential, logarithmic, trigonometric, and hyperbolic functions; integration techniques; indeterminate forms; Taylor's Theorem; and infinite series. (Prerequisite: MA 171 or equivalent) Four credits.

MA 231 Discrete Mathematics
Topics in this course include logic; sets; functions; equivalence relations and partitions; factor sets; mathematical induction; isomorphisms; and countability. Also listed as CS 231. Three credits.

MA 235 Linear Algebra
Students examine linear spaces and subspaces; linear independence and dependence; bases and dimension; linear operators; matrix theory; determinants and systems of linear equations; eigenvalues and eigenvectors. (Prerequisite: MA 231) Three credits.

MA 271 Multivariable Calculus I
Topics in this course include convergence tests, power series; vectors in the plane and in three-space; arc length, curvature, equations of lines and planes; vector functions; parametric equations; functions of several variables, differentiability, gradient, directional derivatives; tangent planes, normal lines; total differential, extrema; Lagrange multipliers; sequences and series. (Prerequisite: MA 172 or equivalent) Three credits.

MA 272 Multivariable Calculus II
This course covers multiple integration: volume and surface integrals in cartesian, cylindrical, and spherical coordinates; line integrals; Green's theorem; divergence and curl, Jacobians; change of variables; Stokes's theorem; and divergence theorem. (Prerequisite: MA 271 or equivalent) Three credits.

MA 331 Applied Mathematics I
This course covers the theory and solution of ordinary differential equations: first-order equations, linear equations of arbitrary order, and linear systems; Gamma and Bessel functions; Chebyshev, Legendre, Laguerre, and Hermite polynomials; Green's identities, Stokes's and Gauss's theorems; and calculus of variations. (Prerequisites: MA 235, and MA 272, or permission of the department chair) Three credits.

MA 332 Applied Mathematics II
This course continues MA 331 and offers a more theoretical approach to the subject material. Topics include Fourier series, orthogonal functions, normed linear spaces; adjoint operators, Sturm-Liouville problems; partial differential equations: the heat, wave, and Laplace equations; separation of variables; and the method of characteristics. (Prerequisite: MA 331, or MA 321 and four semester of calculus, or permission of the department chair) Three credits.

MA 334 Abstract Algebra
Students examine group theory, rings and ideals, integral domains, and fields. (Prerequisites: MA 272 and MA 235, or permission of the department chair) Three credits.

MA 337 Number Theory
This study of the integers includes but is not limited to: primes and their distribution, divisibility and congruences, quadratic reciprocity, special numerical functions such as Euler's one-function, and Diophantine equations. Students consider the influence number theory has had on the development of algebra and the interplay between the two. (Prerequisites: MA 231 and MA 272, or permission of the department chair) Three credits.

MA 341 Linear Programming and Operations Research
Topics in this course include convex sets, extreme points, theoretical basis of the simplex method for linear programming, the simplex computational procedure, duality theory, and sensitivity analysis. The course also covers transportation problem and network applications as time permits. (Prerequisites: MA 235, and MA 272, or permission of the department chair) Three credits.

MA 342 Theory of Computation
This course covers finite state machines, push-down automata, Turing machines and recursive functions; mechanisms for formal languages: regular grammars, context-free grammars, context-sensitive grammars; decidable versus undecideable problems; and presents an introduction to algorithm analysis. Also listed as CS 342. (Prerequisite: MA 231 or permission of the department chair) Three credits.

MA 351 Probability and Statistics I
Topics in this course include counting techniques, axiomatic probability theory; discrete and continuous sample spaces; random variables, distribution functions, probability density and mass functions; normal, binomial, and Poisson distributions; and limit laws. (Prerequisite: MA 272 and MA 231 or permission of the department chair) Three credits.

MA 352 Probability and Statistics II
This course covers joint and continuous distributions; statistical application of probability; theory of sampling; variances of sums and averages; estimation and hypothesis testing; and least squares, curve-fitting, and regression. (Prerequisite: MA 351 or permission of the department chair) Three credits.

MA 361 Topics in Algebra
This course investigates three topics in greater depth than can be done in the first linear or abstract algebra course. Topics may include canonical forms for matrices, metric linear algebra, ideal theory, finite non-abelian groups, and Galois theory. The course typically includes one linear and one abstract algebra topic. (Prerequisite: MA 334 or permission of the department chair) Three credits.

MA 371 Real Analysis
This course examines R as a complete, ordered, archimedian field; R as a linear vector space equipped with inner product and norm; metrics, particularly Euclidean, on R, topological concepts: continuity, connectedness, and compactness; the intermediate value, extreme value, monotone convergence, Bolzano/Weierstrass and Heine/Borel theorems; convergence and uniform convergence of sequences of continuous functions; differentiation: the mean value, implicit and inverse function theorems. (Prerequisites: MA 231 and MA 272, or permission of the department chair) Three credits.

MA 373 Complex Analysis
Topics in this course include algebra of complex numbers, Cauchy-Riemann equations and analytic functions, complex differentiation, integration in the complex plane, Cauchy's Theorem and integral formula, conformal mapping, Laurent series and residue theory, and applications. (Prerequisite: MA 371 or permission of the department chair) Three credits.

MA 377 Numerical Analysis
This course investigates computer arithmetic, round-off errors, the solution of nonlinear equations, polynomial approximation, numerical differentiation and integration, and the solution of systems of linear equations via student-written code to implement the algorithms and/or the use of available software. Also listed as CS 377. (Prerequisites: MA 172, MA 235, and proficiency in a computer language, or permission of the department chair) Three credits.

MA 383 Modern Geometry
Topics in this course include: foundation for plane geometries; theorems of Menelaus, Ceva, Desargues, Pascal, Brianchon, and Feuerbach; inversion and reciprocation transformations; projective, Riemannian and Lobachevskian geometries; and Poincarè model. (Prerequisite: MA 231 or permission of the department chair) Three credits.

MA 385 Point Set Topology
This course considers topological spaces, continuous functions; product, metric, and quotient spaces; countability and separation axioms; existence and extension of continuous functions; compactification; metrization theorems and complete metric spaces. (Prerequisite: MA 371 or permission of the department chair) Three credits.

MA 390-391 Honors Seminar
Participation is open to senior mathematics majors with a 3.50 or higher GPA in mathematics and invited junior and senior mathematics majors with demonstrated ability who have been recommended by the mathematics faculty. This seminar provides talented students with an opportunity to undertake individualized study under faculty direction. Participants present several reports on their findings before a group of peers. The seminar's subject matter varies yearly. Three credits per semester.

MA 397-398 Internship in Mathematics
The internship program provides senior mathematics majors with opportunities to gain practical, career-related experience in a variety of supervised field settings. Student interns select from a variety of placements, especially those requiring applications of mathematics, numerical methods, and statistics. Interns spend a minimum of 10 hours per week working at the placement site and complete the required academic component specified by their faculty advisor. Internship credits vary; interns may register for a summer session and/or one or two semesters for an overall maximum of six credits. In addition, an internship must satisfy the requirements outlined in the University Internship Policy, which is available from the Career Planning Center. (Prerequisites: senior standing, completed application form, acceptance by the field placement supervisor, and approval by the Department of Mathematics and Computer Science.) One to three credits per semester/session.

MA 399 Independent Study in Mathematics
Independent study provides students with the opportunity to examine areas not covered in the undergraduate curriculum. Under the guidance of a faculty member, advanced students learn about an area in mathematics through reading and research. Independent study includes written work in the form of exercises or papers. Students apply to a professor under whose direction they wish to study and obtain the approval of the department chair. This course may not replace a mathematics elective to fulfill the requirements for the major. Three credits.